Answer to Question #100862 in Molecular Physics | Thermodynamics for Pham Anh Khoa

Question

An ideal gas (γ = 1.40) expands slowly and adiabatically. If the final temperature is one third the initial temperature, by what factor does the volume change?

Answer 1

According to the adiabatic equation:

$$T_1V_1^{\gamma-1} = T_2V_2^{\gamma-1}$$

$${T_1 \over T_2} = {V_2^{\gamma-1} \over V_1^{\gamma-1}}$$

If the final temperature was one third of the initial, then:

$$3 = {V_2^{\gamma-1} \over V_1^{\gamma-1}}$$

If γ = 1.40:

$$3 = {V_2^{0.4} \over V_1^{0.4}}$$

$$15.5885^{0.4} = {V_2^{0.4} \over V_1^{0.4}}$$

$$15.5885 = {V_2\over V_1}$$

That is, the gas expands 15.5885 times, compared with the initial volume.